Material Parameters Determining the Band Gaps of Solid-Solid Phononic Crystals

Abstract

Material parameters directly determining band gaps for general threedimensional phononic crystals are derived from the basic wave equations. These parameters include the mass density ratio, shear modulus ratio and Poissons ratios of the scatterer and matrix materials. The effects of these parameters on phononic band gaps are discussed by computing two-dimensional systems with different filling fractions and lattice forms for both anti-plane and in-plane wave modes. The results show that the mass density ratio predominantly determines the band gap for the anti-plane mode, while that both mass density ratio and shear modulus ratio play equally important roles in controlling the band gaps for the in-plane mode. The maximum band gap will appear at both large density ratio and shear modulus ratio for either anti-plane or in-plane wave mode; but band gaps may appear in other situations depending on the filling fraction and lattice forms. Unlike one-dimensional phononic crystals, neither acoustic impedance ratio nor wave velocity ratio of the two-dimensional systems can determine the band gap independently. The analysis of the paper is relevant to the tuning of band gaps.